Calculus Examples

$\frac{\frac{2}{x^{2}}}{\frac{10}{x^{5}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{x^{2}} \cdot \frac{x^{5}}{10}$

Step 2

Combine.

$\frac{2 x^{5}}{x^{2} \cdot 10}$

Step 3

Cancel the common factor of $2$ and $10$ .

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Step 3.1

Factor $2$ out of $2 x^{5}$ .

$\frac{2 (x^{5})}{x^{2} \cdot 10}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $x^{2} \cdot 10$ .

$\frac{2 (x^{5})}{2 (x^{2} \cdot 5)}$

Step 3.2.2

Cancel the common factor.

$\frac{2 x^{5}}{2 (x^{2} \cdot 5)}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{5}}{x^{2} \cdot 5}$

$\frac{x^{5}}{x^{2} \cdot 5}$

$\frac{x^{5}}{x^{2} \cdot 5}$

Step 4

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 4.1

Factor $x^{2}$ out of $x^{5}$ .

$\frac{x^{2} x^{3}}{x^{2} \cdot 5}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x^{2}$ out of $x^{2} \cdot 5$ .

$\frac{x^{2} x^{3}}{x^{2} (5)}$

Step 4.2.2

Cancel the common factor.

$\frac{x^{2} x^{3}}{x^{2} \cdot 5}$

Step 4.2.3

Rewrite the expression.

$\frac{x^{3}}{5}$

$\frac{x^{3}}{5}$

$\frac{x^{3}}{5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$